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Find the least common multiple of xy (k2 + 1) + k(x2 + y2) and xy(k2 – 1) + k (x2 – y2)

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Best answer

xy (k2 + 1) + k(x2 + y2) = k2 xy + xy + kx2 + ky2

= (k2 xy + kx2) + (ky2 + xy)

= kx(ky + x) + y (ky + x)

= (ky + x) (kx + y)

xy (k2 – 1) + k(x2 – y2) = k2 xy – xy + kx2 – ky2

= (k2xy + kx2) – xy – ky2

= kx(ky + x) -y (ky + x)

= (ky + x) (kx – y)

L.C.M. = (ky + x) (kx + y) (kx – y)

= (ky + x) (k2 x2 – y2)

The least common multiple is (ky + x) (k2 x2 – y2)

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